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Dancing Solution Curves of ODEs

Dancing Solution Curves of ODEs
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2019-09-08 11:50
FunctionCalculusOptimizationParametric EquationSlider Animation
This example demonstrates the dynamic dancing effect of solution curves of ordinary differential equations (ODEs) as parameters vary. Key math concepts include ODEs, slope fields, solution curves, and parametric animation. Constructed using GeoGebra commands like SolveODE, SlopeField, t, f, button1, Ax, Ay, A, sol, n, speed, slp, and numerous objects A1-A18, B1-B11. Suitable for university students in mathematics or physics to study numerical solutions and visualizations of ODEs, or for educational demonstrations.

GeoGebra Commands & Parameters

  1. SolveODE(f(x, y), Ax, Ay, 100, 0.08) → sol
  2. SlopeField(f) → slp
  3. SolveODE(f(x, y), Ax, Ay + 0 - 0.8, 100, 0.08) → A1
  4. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (2 - 1)) - 0.8, 100, 0.08) → A2
  5. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (3 - 1)) - 0.8, 100, 0.08) → A3
  6. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (4 - 1)) - 0.8, 100, 0.08) → A4
  7. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (5 - 1)) - 0.8, 100, 0.08) → A5
  8. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (6 - 1)) - 0.8, 100, 0.08) → A6
  9. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (7 - 1)) - 0.8, 100, 0.08) → A7
  10. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (8 - 1)) - 0.8, 100, 0.08) → A8
  11. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (9 - 1)) - 0.8, 100, 0.08) → A9
  12. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (10 - 1)) - 0.8, 100, 0.08) → A10
  13. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (11 - 1)) - 0.8, 100, 0.08) → A11
  14. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (12 - 1)) - 0.8, 100, 0.08) → A12
  15. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (13 - 1)) - 0.8, 100, 0.08) → A13
  16. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (14 - 1)) - 0.8, 100, 0.08) → A14
  17. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (15 - 1)) - 0.8, 100, 0.08) → A15
  18. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (16 - 1)) - 0.8, 100, 0.08) → A16
  19. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (17 - 1)) - 0.8, 100, 0.08) → A17
  20. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (18 - 1)) - 0.8, 100, 0.08) → A18
  21. SolveODE(f(x, y), Ax, Ay + 0 - 0.8, -100, 0.08) → B1
  22. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (2 - 1)) - 0.8, -100, 0.08) → B2
  23. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (3 - 1)) - 0.8, -100, 0.08) → B3
  24. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (4 - 1)) - 0.8, -100, 0.08) → B4
  25. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (5 - 1)) - 0.8, -100, 0.08) → B5
  26. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (6 - 1)) - 0.8, -100, 0.08) → B6
  27. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (7 - 1)) - 0.8, -100, 0.08) → B7
  28. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (8 - 1)) - 0.8, -100, 0.08) → B8
  29. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (9 - 1)) - 0.8, -100, 0.08) → B9
  30. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (10 - 1)) - 0.8, -100, 0.08) → B10
  31. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (11 - 1)) - 0.8, -100, 0.08) → B11
  32. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (12 - 1)) - 0.8, -100, 0.08) → B12
  33. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (13 - 1)) - 0.8, -100, 0.08) → B13
  34. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (14 - 1)) - 0.8, -100, 0.08) → B14
  35. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (15 - 1)) - 0.8, -100, 0.08) → B15
  36. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (16 - 1)) - 0.8, -100, 0.08) → B16
  37. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (17 - 1)) - 0.8, -100, 0.08) → B17
  38. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (18 - 1)) - 0.8, -100, 0.08) → B18

AI Drawing Prompt Reference

Draw a set of solution curves for ordinary differential equations to demonstrate their dynamic dancing effect as parameters vary. Start by plotting the base solution curve, then generate multiple solution curves based on it, adjusting the slope parameters to make them dynamically change around the base curve, creating a dancing effect. Also display the slope field as a background to help understand the dynamic variation of the solution curves.
The prompt above was compiled from the original drawing commands and is for reference only.